Appendix C : Regression Analysis Results for the Inverse Model

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(Note: All output parameters are Relative to those for d10h08e10f10.)


Inverse Equations Using Pressure Only

Y-Var R^2 Adj R^2 StdErrY n X-Vars Coeff. Std Err t-Stat P-value
F 0.999 0.999 0.009 29 Intercept 0.00305 0.0043 0.701 4.89E-01
          Base 0.99661 0.0056 178.132 5.38E-43
t 0.810 0.803 0.281 29 Intercept -0.00922 0.1824 -0.051 9.60E-01
          Curve^(-1.82)*Base^(-2) 1.43786 0.1338 10.744 2.98E-11
d 0.790 0.755 0.170 29 Intercept -1.31117 0.3157 -4.154 3.57E-04
          Amp -1.70738 0.4298 -3.973 5.65E-04
          Amp^(1/2) 2.97558 0.5937 5.012 4.03E-05
          Stdev 0.78820 0.0913 8.632 8.00E-09
          Stdev*Base^(-1) 0.27815 0.0523 5.320 1.85E-05
d 0.920 0.902 0.115 22 Intercept -2.06847 0.2622 -7.889 4.41E-07
(E>=10)         Amp -1.87677 0.3613 -5.194 7.31E-05
          Amp^(1/2) 3.59001 0.4854 7.396 1.04E-06
          Stdev 0.98231 0.0791 12.420 5.93E-10
          Stdev*Base^(-1) 0.35933 0.0470 7.645 6.74E-07
h 0.824 0.795 0.150 29 Intercept 2.13050 0.2785 7.651 6.89E-08
          Amp 1.25209 0.3792 3.302 3.00E-03
          Amp^(1/2) -2.66120 0.5238 -5.081 3.39E-05
          Stdev 0.31393 0.0805 3.897 6.83E-04
          Stdev*Base^(-1) -0.24291 0.0461 -5.266 2.12E-05
h 0.957 0.946 0.084 22 Intercept 2.92973 0.1904 15.387 2.07E-11
(E>=10)         Amp 1.63731 0.2624 6.240 8.97E-06
          Amp^(1/2) -3.51994 0.3525 -9.986 1.58E-08
          Stdev 0.07444 0.0574 1.296 2.12E-01
          Stdev*Base^(-1) -0.28473 0.0341 -8.341 2.06E-07
E^(-2/3) 0.649 0.591 0.106 29 Intercept 0.19158 0.0838 2.287 3.13E-02
          Amp*Base^(-1) -0.33779 0.0704 -4.797 6.96E-05
          Stdev*Base^(-1) -0.08774 0.0298 -2.949 7.01E-03
          Stdev^(-1) 0.43683 0.0964 4.529 1.37E-04
          Amp^(-1) 0.00348 0.0016 2.222 3.59E-02
E^(-2/3) 0.960 0.880 0.053 7 Intercept 0.22982 0.1469 1.565 2.58E-01
(E < 10)         Amp*Base^(-1) -0.72528 0.1360 -5.332 3.34E-02
          Stdev*Base^(-1) -0.23342 0.0386 -6.055 2.62E-02
          Stdev^(-1) 0.86471 0.1896 4.561 4.49E-02
          Amp^(-1) 0.00610 0.0012 5.018 3.75E-02


Inverse Equations Using Pressure and Probe Displacement

Y-Var R^2 Adj R^2 StdErrY n X-Vars Coeff. Std Err t-Stat P-value
t 0.990 0.989 0.065 29 Intercept 0.06469 0.0372 1.737 9.37E-02
          DispB^(4/3)*Base^(-1) 1.21924 0.0238 51.234 1.95E-28
d 0.925 0.912 0.102 29 Intercept 0.28818 0.0916 3.146 4.38E-03
          DispA*Base^(-1) -1.55673 0.1717 -9.068 3.21E-09
          DispA^(1/2)*Base^(-1) 1.53099 0.2745 5.577 9.72E-06
          DispB^(4/3)*Base^(-1) 1.19363 0.0778 15.337 6.69E-14
          Base^(-1) -0.48869 0.1066 -4.584 1.20E-04
d 0.966 0.958 0.075 22 Intercept 0.24960 0.0803 3.109 6.39E-03
(E>=10)         DispA*Base^(-1) -1.66882 0.1330 -12.551 5.05E-10
          DispA^(1/2)*Base^(-1) 1.41932 0.2228 6.369 6.99E-06
          DispB^(4/3)*Base^(-1) 1.36198 0.0664 20.524 1.96E-13
          Base^(-1) -0.44090 0.0880 -5.011 1.07E-04
h 0.800 0.776 0.157 29 Intercept 0.19376 0.1046 1.852 7.58E-02
          DispA 1.28240 0.1762 7.276 1.27E-07
          DispB^(4/3) -0.96869 0.1631 -5.939 3.37E-06
          DispB^(4/3)*Base^(-1) 0.34749 0.0993 3.501 1.76E-03
h 0.882 0.863 0.134 22 Intercept 0.30714 0.1012 3.035 7.12E-03
(E>=10)         DispA 1.52948 0.1624 9.416 2.23E-08
          DispB^(4/3) -1.15418 0.1533 -7.527 5.77E-07
          DispB^(4/3)*Base^(-1) 0.26716 0.0985 2.713 1.43E-02
E^(-2/3) 0.724 0.691 0.092 29 Intercept -0.12252 0.0733 -1.672 1.07E-01
          DispA^(-2)*Base^2 -0.52912 0.0747 -7.080 2.02E-07
          DispB^(-4/3)*Base 1.03923 0.1483 7.009 2.40E-07
          DispA^(-2)*DispB^(-4/3)*Base^2 -0.14897 0.0464 -3.212 3.61E-03
E^(-2/3) 0.981 0.942 0.037 7 Intercept -0.36044 0.1009 -3.573 7.02E-02
(E < 10)         DispA^(-2)*Base^2 -0.73990 0.1367 -5.411 3.25E-02
          DispB^(-4/3)*Base 1.89831 0.1914 9.917 1.00E-02
          DispA^(-2)*DispB^(-4/3)*Base^2 -0.67003 0.1330 -5.036 3.72E-02
          DispA^(-2)*DispB^(-4/3)*Base 0.05017 0.0191 2.627 1.20E-01

DispA : Probe Displacement at x = 0 cm        DispB : Probe Displacement at x = 2.8 cm